Question: What do the following two equations represent? $-x+3y = 1$ $3x-9y = 5$
Solution: Putting the first equation in $y = mx + b$ form gives: $-x+3y = 1$ $3y = x+1$ $y = \dfrac{1}{3}x + \dfrac{1}{3}$ Putting the second equation in $y = mx + b$ form gives: $3x-9y = 5$ $-9y = -3x+5$ $y = \dfrac{1}{3}x - \dfrac{5}{9}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.